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Volume 42, Issue 2
A Scalar Auxiliary Variable (SAV) Finite Element Numerical Scheme for the Cahn-Hilliard-Hele-Shaw System with Dynamic Boundary Conditions

Changhui Yao, Fengdan Zhang & Cheng Wang

DOI: 10.4208/jcm.2205-m2021-0234

J. Comp. Math., 42 (2024), pp. 544-569.

Published online: 2024-01

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  • Abstract

In this paper, we consider the Cahn-Hilliard-Hele-Shaw (CHHS) system with the dynamic boundary conditions, in which both the bulk and surface energy parts play important roles. The scalar auxiliary variable approach is introduced for the physical system; the mass conservation and energy dissipation is proved for the CHHS system. Subsequently, a fully discrete SAV finite element scheme is proposed, with the mass conservation and energy dissipation laws established at a theoretical level. In addition, the convergence analysis and error estimate is provided for the proposed SAV numerical scheme.

  • Keywords

Cahn-Hilliard-Hele-Shaw system, Dynamic boundary conditions, Bulk energy and surface energy, Scalar auxiliary variable formulation, Energy stability, Convergence analysis.

  • AMS Subject Headings

65N06, 65B99

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-42-544, author = {Yao , ChanghuiZhang , Fengdan and Wang , Cheng}, title = {A Scalar Auxiliary Variable (SAV) Finite Element Numerical Scheme for the Cahn-Hilliard-Hele-Shaw System with Dynamic Boundary Conditions}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {42}, number = {2}, pages = {544--569}, abstract = {

In this paper, we consider the Cahn-Hilliard-Hele-Shaw (CHHS) system with the dynamic boundary conditions, in which both the bulk and surface energy parts play important roles. The scalar auxiliary variable approach is introduced for the physical system; the mass conservation and energy dissipation is proved for the CHHS system. Subsequently, a fully discrete SAV finite element scheme is proposed, with the mass conservation and energy dissipation laws established at a theoretical level. In addition, the convergence analysis and error estimate is provided for the proposed SAV numerical scheme.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2205-m2021-0234}, url = {http://global-sci.org/intro/article_detail/jcm/22891.html} }
TY - JOUR T1 - A Scalar Auxiliary Variable (SAV) Finite Element Numerical Scheme for the Cahn-Hilliard-Hele-Shaw System with Dynamic Boundary Conditions AU - Yao , Changhui AU - Zhang , Fengdan AU - Wang , Cheng JO - Journal of Computational Mathematics VL - 2 SP - 544 EP - 569 PY - 2024 DA - 2024/01 SN - 42 DO - http://doi.org/10.4208/jcm.2205-m2021-0234 UR - https://global-sci.org/intro/article_detail/jcm/22891.html KW - Cahn-Hilliard-Hele-Shaw system, Dynamic boundary conditions, Bulk energy and surface energy, Scalar auxiliary variable formulation, Energy stability, Convergence analysis. AB -

In this paper, we consider the Cahn-Hilliard-Hele-Shaw (CHHS) system with the dynamic boundary conditions, in which both the bulk and surface energy parts play important roles. The scalar auxiliary variable approach is introduced for the physical system; the mass conservation and energy dissipation is proved for the CHHS system. Subsequently, a fully discrete SAV finite element scheme is proposed, with the mass conservation and energy dissipation laws established at a theoretical level. In addition, the convergence analysis and error estimate is provided for the proposed SAV numerical scheme.

Yao , ChanghuiZhang , Fengdan and Wang , Cheng. (2024). A Scalar Auxiliary Variable (SAV) Finite Element Numerical Scheme for the Cahn-Hilliard-Hele-Shaw System with Dynamic Boundary Conditions. Journal of Computational Mathematics. 42 (2). 544-569. doi:10.4208/jcm.2205-m2021-0234
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